The GW constraints on the Lorentz-violating dispersion relation has been analyzed by comparing the modified waveform (REF ) with the GW strain data in GWTC-1 [1]}, GWTC-2 [2]}, and GWTC-3 [3]}. The gravitational constraint on \({\cal W}_2 - {\cal G}_2\)  can be obtained from the posterior samples of the Lorentz-violating parameter \(A_{4}\)  in [1]}, [2]}, [3]}. In [1]}, [2]}, [3]}, the Lorentz-violating parameter \(A_4\)  is sampled separately for \(A_4>0\)  and \(A_4<0\)  in [1]}, [2]}, [3]}. Here we consider positive and negative \(A_4\)  separately as well and derive the corresponding bounds on \({\cal W}_2 - {\cal G}_2\) , which are presented in Table. REF . From this table, it is shown that the most stringent constraint is from the combined posterior of GW events in GWTC-3, which gives
\(| {\cal W}_2- {\cal G}_2 |< 1.2 \times 10^{-10} \; {\rm m}^2 \nonumber \\\) 
